Φ index: A standardized scale-independent citation indicator

Any average quantity can experience strong fluctuations due to outliers, an effect that grows with decreasing sample size. Thus, size-normalized quantities are not truly size-independent. For citation averages, such as Impact Factors (IF), this effect causes distortions that routinely plague journal IF rankings [1]. The Central Limit Theorem, which underlies this effect, also allows us to standardize citation averages and remove the scale dependence. We thus propose the Φ index, a standardized citation impact indicator that is analogous to the Z-score in statistics. Apart from being scale-independent, the Φ index can also account for different citation practices across research areas, which allows us to compare journals of different sizes and subjects. The Φ index can be readily generalized to other citation averages used to compare research areas, university departments or countries in various types of rankings.

[1] M. Antonoyiannakis, Quantitative Science Studies 1, 639 (2020)